We have studied the effect of the pH and surface charge of mica on the adsorption of the positively charged weak polyelectrolyte (PE) poly(2-vinylpyridine) (P2VP) using atomic force microscopy (AFM) single-molecule experiments. These AFM experiments were performed in situ directly under aqueous media. If the mica's surface and the PE are oppositely charged (pH > 3), the PE forms a flat adsorbed layer of two-dimensionally (2D) equilibrated self-avoiding random walk coils. The adsorbed layer's structure remains almost unchanged if the pH is decreased to pH 3 (the mica's surface is weakly charged). At pH 2 (the mica surface is decorated by spots of different electrical charges), the polyelectrolyte chains take the form of a 2D compressed coil. In this pH range, at an increased P2VP concentration in solution, the PE segments preferentially adsorb onto the top of previously adsorbed segments, rather than onto an unoccupied surface. We explain this behavior as being caused by the heterogeneous character of the charged surface and the competitive adsorption of hydronium ions. The further increase of polymer concentration results in a complete coverage of the mica substrate and the charge overcompensation by P2VP chains adsorbed on the similarly charged substrate, due to van der Waals forces.